Suppose that f is a meromorphc function with order σ(f) and lower order μ(f). Suppose that P[f] is a differential polynomial of f. In this paper, it is shown that the order and the lower order of P[f] are equal to the order and the lower order of f under certain conditions on the degree of the differential polynomial P[f], i.e., σ(P)=σ(f) and μ(P)=μ(f). This result improves previous results.